Apparatus and methods for reducing optical distortion in an optical system by thermal means are disclosed. The apparatus includes a heating/cooling system spaced apart from and in thermal communication with an internally reflecting surface of a refractive element in the optical system. The heating/cooling system is adapted to create a select temperature distribution in the refractive optical element near the internally reflecting surface to alter the refractive index and/or the surface profile in a manner that reduces residual distortion.
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7. A method of reducing distortion in an optical system having a refractive optical element with an index of refraction, and an internally reflecting surface with a surface profile, the method comprising:
arranging a heating/cooling system spaced apart from but in thermal communication with the internally reflecting surface; and using the heating/cooling system, creating a select temperature distribution in the refractive optical element near the internally reflecting surface to alter the refractive index and/or the surface profile to reduce residual distortion.
1. An apparatus for reducing residual distortion in an optical system having a refractive optical element with an internally reflecting surface, a surface profile and a refractive index, the apparatus comprising:
a heating/cooling system spaced apart from but in thermal communication with the internally reflecting surface; and wherein the heating/cooling system is adapted to create a select temperature distribution in the refractive optical element near the internally reflecting surface to alter the refractive index and/or the surface profile in a manner that reduces the residual distortion in the optical system.
2. The apparatus of
a plurality of individually addressable probes each having a temperature; and a controller coupled to the probes, the controller adapted to control the temperature of each probe.
3. The apparatus of
4. The apparatus of
5. The apparatus of
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1. Field of the Invention
The invention relates to optical systems, and in particular it relates to apparatus and methods for reducing optical distortion in optical systems using thermal means.
2. Description of the Prior Art
Essentially all optical systems have imaging imperfections referred to in the art as "aberrations". There are an infinite number of possible aberrations, each varying in a different way with the field position and aperture size of the optical system. Generally it is the low order aberrations that prevail. Depending on the type of optical system, some aberrations are more prevalent than others. Examples of types of aberrations are spherical aberration, coma, astigmatism, field curvature, and distortion. Aberrations can arise for a number of reasons. For example, certain aberrations are inherent in the optical design, which typically assumes perfectly made and positioned optical elements. Other aberrations arise as a result of imperfections in the manufacturing and assembly of the optical system. For example, deviations in the surface curvature, variations in the surface shape (e.g., undulations, grooves, etc.), variations in refractive index, and variations in the spacing, centering and tilt from the ideal design are all potential sources of aberrations.
By virtue of the optical design, the aberrations in the system will have different sensitivities to certain departures from perfection--i.e., some departures from perfection on some elements contribute more to certain aberrations than other departures. Accordingly, different fabrication and alignment tolerances are placed on different elements.
In many optical systems, distortion is particularly problematic. Distortion is defined as the variation of an image point location from its ideal location as a function of field position. Included in the definition of distortion is magnification error, which is a linear change in the position of points in the image with the distance from the center of the field.
Distortion cannot be corrected at the pupil because each point in the field shares the pupil and any correction at the pupil would produce the same effect over the entire field.
By way of example, in a folded projection optical system, out-of-plane deviations in a folding surface located between the focal planes and the pupil can cause distortion in the image. Distortion arising from the folding surface imperfections can be static, such as those caused by surface figuring errors, or dynamic such those caused by warping of the folding surface by thermal transients. While great pains can be taken to minimize distortion in the optical design, in practice it is very difficult to reduce distortion to tolerable amounts due to fabrication and assembly errors, as well as from environmental effects.
For example, controlling distortion in optical lithography lenses is of extreme importance because different lithography systems are used to image different layers, and small image placement errors ultimately result in the circuit feature produced by one layer failing to connect properly with that of another layer.
An example optical lithography lens system is the Wynne-Dyson system, such as described in U.S. Pat. No. 4,391,494 (hereinafter, "the '494 patent"), which patent is incorporated herein by reference. The Wynne-Dyson system is a symmetric system having two folding surfaces located close to and equidistant from the object and image planes. Theoretically this design has no distortion of any order because of its symmetrical nature. In practice the folding surfaces, which are internal reflecting surfaces of respective prisms, are the major contributors to image distortion. If the imperfections of the folding surfaces could be made identical then the distortion contributions from the two prisms would be equal and opposite and would cancel. However, in practice figure matching is never perfect and the residual errors contribute substantially to the total distortion observed in the image.
Other sources of distortion include refractive index inhomogeneities in the glasses used in the prisms and the refractive lenses as well as the surface figures of the other refractive components. In practice, distortions as large as 100 nm are possible. The main reason the prism hypotenuse surfaces produce most of the image distortion is because they act as a internally reflecting surface that produces an effect on the reflected wavefront equal to double the index of refraction multiplied by the prism surface imperfection.
One approach used to correct residual amounts of aberrations in optical systems is through the use of adaptive optics. US Pat. No. 4,773,748 to Shih et al. discloses a deformable mirror system for reducing distortion in a projected image. However, this system relies on using a mirror made up of two sheets of material having different coefficients of expansion and an array of electrical resistors to heat the mirror to physically distort the reflective surface. Such a system is not amenable or adaptable for use in certain types of optical systems such as the Wynne-Dyson system because there is no suitable location in the system for such a mirror. Further, there can be no physical contact with the internally reflecting surface of the Wynne-Dyson prism because such contact adversely affects the internal reflection properties of the prism.
While totally eliminating residual distortion from an optical system is probably an impractical pursuit, many optical systems--and particularly optical lithography systems with refractive elements--would greatly benefit from apparatus and methods that result in significant reductions in distortion.
A first aspect of the invention is an apparatus for reducing residual distortion in an optical system. The optical system in question has a refractive optical element, such as a prism, having an internally reflecting surface, a surface profile and a refractive index. The apparatus includes a heating/cooling system spaced apart from but in thermal communication with the internally reflecting surface. The heating/cooling system is adapted to create a select temperature distribution in the refractive optical element near the internally reflecting surface to alter the refractive index and/or the surface profile in a manner that reduces the residual distortion.
A second aspect of the invention is a method of reducing distortion in the aforementioned optical system. The method includes arranging a heating/cooling system spaced apart from but in thermal communication with the internally reflecting surface, and then using the heating system to create a select temperature distribution in the refractive optical element near the internally reflecting surface to alter the refractive index and/or the surface profile to reduce residual distortion.
In the following detailed description of the embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims.
Example Optical System
With reference to
Optical system 8 includes a concave spherical mirror 10, an aperture stop AS1 located at the mirror, a refractive lens group 11, and a prism assembly 12. Prism assembly 12 includes symmetric fold prisms 15A and 15B having respective internal reflecting surfaces 16A and 16B. Prism 15A also has a reticle-wise surface 17A and a mirror-wise surface 18A. Likewise, prism 15B has wafer-wise surface 17B and mirror-wise surface 18B. Symmetric fold prisms 15A and 15B are used to attain sufficient working space for movement of a reticle R held in an object plane OP1, and a wafer W held in an image plane IP1. Arranged adjacent prism assembly 12 and in thermal communication with surface 16B is a heating/cooling system 20, discussed in greater detail below.
Mirror 10, lens group 11 and prism assembly 12 are disposed symmetrically about an optical axis 22. Optical system 8 is essentially symmetrical relative to aperture stop AS1 located at mirror 10 so that the system is initially corrected for coma, distortion, and lateral color.
In optical system 8, refractive lens group 11 and prism assembly 12, in conjunction with mirror 10, in theory correct the remaining optical aberrations, which include axial color, astigmatism, Petzval or field curvature, and spherical aberration.
In optical system 8, an ideal ray 30 (solid line) originates from a point on reticle R, enters prism 15A at surface 17A, internally reflects within prism 15A at surface 16A, and exits prism surface 18A. Ray 30 continues through the upper portion of refractive lens group 11, reflects from mirror 10, passes back through the lower portion the refractive lens group 11, enters prism 15B at surface 18B, internally reflects within the prism at surface 16B, exits the prism at surface 17B, and reaches wafer W.
In theory the position of ideal ray 30 on wafer W should be the exact symmetrical opposite position as its origin point on reticle R. In practice, however, imperfections in the optical system cause ray 30 to deviate from an ideal path. The actual ray path is indicated by ray 32 (dashed line). In practice, upon entering prism 15A at surface 17A, small variations in the refractive index and the flatness of surface 16A cause ray 32 to deviate from the ideal path represented by ideal ray 30. Ray 32 internally reflects from side 16A, and then passes through the remaining portion of prism 15A. Again, after returning to bottom prism 15B, variations in the refractive index of the prism and the flatness of surface of surface 17A cause ray 32 to deviate even more from the path of ideal ray 30 as is travels between side 16B and surface 17B.
Generalized Heating System Embodiment
In a general embodiment, heating/cooling system includes a controller 90 coupled to a heating/cooling unit 94. Heating/cooling unit 94 is in thermal communication with optical element 80, as indicated by heat transfer 95. Heating/cooling unit 94 is separated from surface 82 of optical element 80 by a gap G having a width WG. The main mechanism for heat transfer 95 is thermal conduction across the very small (e.g. 2-micron) gap G between the heating/cooling unit and the prism face.
Controller 90 provides control signals to heating/cooling unit 94 to cause the heating/cooling unit to deliver/extract heat across gap G to/from surface 82 in a manner that forms a select temperature distribution within optical element 80. The select temperature distribution results in a corresponding select refractive index distribution (variation) and a select surface warp being formed in the material and surface of optical element 80. The select refractive index distribution and warped surface profile act to reduce residual distortion, as described in greater detail below.
In an example embodiment, controller 90 is a computer system that includes a memory unit M, a processor P, a data storage unit U such as a hard disk drive, a programmable current supply 96, and a multiplexer 97, all interconnected. Controller 90 is programmable, such as by inputting instructions recorded on a computer-readable medium CRM (e.g., a floppy disk or a compact disk) into drive D and storing the instructions on data storage unit U. Controller 90 is also adapted to receive (e.g., via CRM) and process (e.g., via processor P) data relating to distortion measurements performed on optical system 8.
Gap G allows heating/cooling unit 94 to be in thermal communication with surface 82 without physically touching the surface. Gap G needs to be large enough so that heating/cooling unit 94 does not significantly affect the internal reflectivity of the surface. In an example embodiment, gap width WG is as small as about 2 microns. Also, because the amounts of heat involved are small as discussed in greater detail below, in an example embodiment heating/cooling unit 94 may provide bursts of heat to different areas of surface 82 in a rapid sequential order rather than to the entire surface simultaneously. This reduces the number of interconnections needed between the heating/cooling unit and the controller, which simplifies the system and reduces cost.
Heating/cooling unit 94 can have any one of a number of different configurations. An example embodiment of a preferred configuration is discussed immediately below.
Example Heating/cooling Unit
In an example embodiment, thermal control plate 110 includes slots 128 formed in upper surface 112 of the thermal control plate and surrounding each probe 102. Slots 128 serve as heat transfer barriers so that the temperature of the end of each probe near the surface 112 is not substantially influenced by the temperatures of adjacent probes. In an example embodiment, the center-to-center spacing of probes 102 is between 4 mm and 10 mm.
If support plate 110 is cooled via coolant flow through cooling channels 116, and no current is applied to resistors 103, then the probe acquires the temperature of the coolant, which is below ambient. In this way, probes 102 can act to selectively cool portions of surface 82. If current is applied to resistors 103, then the temperature along the length of the probe varies from the coolant temperature at the base to the temperature maintained at the probe tip. In this way, probes 102 can act to selective heat portions of surface 82. In an example embodiment, the cooled support plate 110 is maintained at 1°C C. below the ambient temperature and the probes are heated to as much as 1°C C. above the ambient temperature.
In one example embodiment, resistors 103 are each encapsulated in a material (e.g., a potting compound) that is an electrical insulator but a reasonably good thermal conductor to thermally couple the heating element to support plate 110 and minimizes the loss of heat through leads 122A and 122B.
With reference to either of
In example embodiments, support plate 110 is made of either INVAR or a low coefficient of expansion glass/ceramic such as ZERODUR from Schott, ULE from Corning or CLEARCERAM-Z from Ohara. Each of these materials has a relatively low coefficient of expansion so that the shape of the plate is not appreciably deformed by small temperature gradients. This property assists in maintaining a small, uniform air gap G between thermally controlled support plate 110 and refractive element 80.
Example Resistive Element Array
Controller 90 controls the operation of multiplexers 97A and 97B, and programmable power supply 96. In an example embodiment, the current provided to each resistor 103 by current supply 96 is pre-computed by an algorithm that uses the measured image distortion as an input. In an example embodiment, an iterative approach is used to perfect the correction whereby the residual distortion resulting after one correction cycle is corrected by a refined estimate to compensate for residual distortion errors. In an example embodiment, the algorithm also handles imperfections in the operation of the hardware, etc.
Method of Operation
As discussed above, even though optical system 8 (
where:
n is the index of refraction of the glass;
δ is the bump height; and
θ is the angle of incidence on the reflecting surface.
In a typical example where the refractive index is 1.6 and the angle of incidence is 60°C, the effect of a bump is magnified by 1.6 times
Prisms 15A and 15B typically have fixed (static) amounts of refractive index variations and surface shape variations. Further, temperature changes in the prisms resulting from the beginning of an exposure cycle of a batch of wafers create time-varying (dynamic) changes in distortion. One of the advantages of having controller 90 is that the temperature distribution can be quickly changed so that it follows and corrects for both the static and the dynamic changes in distortion. In an example embodiment, controller 90 is coupled to the optical system controller (not shown). In this case, controller 90 knows how much light has flowed through system 8, how much light has been absorbed at the mask and for how long. From this data it can accurately estimated how much heat to apply to prism 15B to achieve dynamic correction of distortion.
Typically, the residual distortion of system 8 has a distortion field 210 that varies in a smooth and continuous manner i.e., a few cycles over the field, such as illustrated in FIG. 5. In such instances, it is possible to further reduce the distortion by introducing a select temperature distribution in prism 15B by heating/cooling the prism at side 16B using heating/cooling system 20 as described above.
In an example embodiment, the reduction in distortion is accomplished by heating/cooling prism 15A at side 16A or prism 15B at side 16B. In another example embodiment, the reduction in distortion is accomplished by heating/cooling both prisms 15A and 15B at respective sides 16A and 16B. The discussion below assumes distortion is corrected by heating prism 15B only; however, the discussion applies equally to heating prism 15A or heating both prisms 15A and 15B.
The temperature distribution imparted to prism 15B is selected to produce, to the extent possible, a refractive index change in the prism, and a surface profile change of the reflective surface that results in an image distortion equal and opposite to the residual image distortion.
Estimating the Temperature Distribution
The image position of an image-forming beam B1 at image plate IP1 such as that shown in
where:
L is the effective depth that the effected temperature distribution extends into the refractive element;
n is the index of refraction of the refractive element;
dT/du is the change in temperature per unit length along the refractive reflecting surface at coordinate u;
F(u) is the footprint size of the beam along the reflecting surface at coordinate u, which is a simple linear function of the coordinate of the position where the center of the beam intersects the surface;
a is the coefficient of expansion of the prism material; and
dn/dT is the change of index of the prism glass with temperature.
The factor of 2 in Equation (2) comes about because the reflected beam passes twice through the element.
Equation (1) indicates that the cosine of the angle of incidence (cosθ) is also a variable. The path length of the beam through the heated part of the refractive element varies as 1/cosθ and the differential change in path varies as cosθ so these two effects cancel each other in Equation (2).
The change in image position dx (i.e., the distortion) is approximated by the equation:
where NA is the numerical aperture of the image-forming beam B1.
Combining equations (2) and (3) and solving for dx yields:
From equation (4) it is readily seen that the distortion is proportional to the temperature gradient (dT/du) as measured along surface coordinate u. It is also clear from
By choosing an appropriate constant of integration C, the average temperature of the temperature distribution can be kept near the ambient temperature, as was done in the example in FIG. 6B.
In the above derivation, the correct sign depends on which prism the temperature correction is made, the sign convention used to define distortion, and the image plane coordinate directions.
An accurate estimate of the temperature distribution required to reduce or cancel a given amount of distortion requires the use of finite element models to solve the resultant temperature distribution, and the deformation of the reflective surface. Distortion dx or g(u) is then calculated using a ray trace program capable of handling an inhomogeneous index distribution and a reflecting surface having a warped surface profile. However, Equation (5) provides a rough estimate, which when used iteratively, results in a substantial reduction in distortion.
A shortcoming of correcting distortion using Equation (5) is the effective heat penetration depth L into the prism, which is assumed to be a constant in the equation, but which really depends on the spatial frequency components of the temperature distribution. High spatial frequency components will not extend into the prism as far as low spatial frequency components. Thus, one avenue to further refine the distortion correction technique based on equation (5) is to apply it to different spatial frequency components using a value of L appropriate to each frequency.
Distortion and Element Temperature Sensitivity
As mentioned above, residual distortion in high-performance optical systems such as optical lithography systems is typically quite small (e.g., typically between about 50 to 150 nanometers). Consequently, effectuating a significant change in the residual distortion (i.e., significantly changing the path length of some rays) requires that only small temperature differences be introduced in the refractive element 80 (e.g., prism 15B).
To illustrate this point, consider the change in path length ΔP for a ray passing through prism 15B and reflecting from surface 16B. ΔP is given by equation (2) above and repeated here for convenience:
By way of example, consider prism 15B to be made of Schott SK-02, an optical glass having an index of refraction n=1.627, a coefficient of thermal expansion a=6.3×10-6 per °C C. and a change of index with temperature (dn/dT) of 4.5×10-6 per °C C. A temperature gradient of 0.1°C C./mm extending over the 10 mm footprint of a 0.32NA beam and into the glass prism for an effective thickness of 6 mm would create a path difference ΔP of:
For an optical system with a numerical aperture NA of 0.35 the image displacement dx is given by equation (3):
This is about 2 times larger than what is typically needed, so that the required temperature gradients are likely to be in the 0.05°C C./mm range and the peak-to-peak temperature differences are likely to be about 1°C C.
Power Requirements
The amount of power required to produce a desired temperature distribution depends upon the area covered and the average temperature gradient desired in the individual probes 102. Assuming that an area 42 mm by 48 mm is covered by a 7×8 element array 100, and that an average 1°C C. temperature difference over a 6 mm probe length is required then the total power P required is given by;
This assumes that the thermal control plate 110 (
While the present invention has been described in connection with preferred embodiments, it will be understood that it is not so limited. On the contrary, it is intended to cover all alternatives, modifications and equivalents as may be included within the spirit and scope of the invention as defined in the appended claims.
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